1. What is Shear Force and Bending Moment?

Definition: Shear force (V) is the internal force parallel to the cross-section of a beam, while bending moment (M) is the internal moment that causes bending.

Purpose: These calculations are essential in structural engineering to ensure beams and other structural elements can withstand applied loads.

2. How Does the Calculator Work?

The calculator uses the fundamental relationship:

Where:

• \( V \) — Shear force (N)
• \( M \) — Bending moment (N m)
• \( x \) — Distance along the beam (m)

Explanation: The shear force is calculated as the rate of change of bending moment with respect to distance along the beam.

3. Importance of These Calculations

Details: Proper calculation of shear force and bending moment is crucial for designing safe and efficient structures that won't fail under load.

4. Using the Calculator

Tips: Enter the distance along the beam, the change in bending moment, and the distance over which this change occurs. The calculator will determine the shear force and bending moment.

5. Frequently Asked Questions (FAQ)

Q1: What's the sign convention for shear force and bending moment?
A: Convention varies, but typically positive shear causes clockwise rotation and positive bending causes tension in the bottom fibers.

Q2: How does distributed load affect these calculations?
A: Distributed loads create continuously varying shear and moment diagrams, requiring integration for exact solutions.

Q3: What's the relationship between shear and moment diagrams?
A: The slope of the moment diagram at any point equals the shear force at that point.

Q4: How do point loads affect the calculations?
A: Point loads cause abrupt changes in shear force and a change in slope of the bending moment diagram.

Q5: What units should I use?
A: Consistent units are essential - typically meters for distance, Newtons for force, and Newton-meters for moments.